Before I Start here is a disclaimer -
I am not a professional CAD or Mechanical Engineer to know much about this. Also, All information I have is from the internet and have NO practical knowledge.

Here we go then.
I am currently working on building a High Performance Free Flow Exhaust for my Bike (Yamaha FZ16 Single 153cc Engine). Attached is the CAD design I made for the Exhaust (I am not a professional CAD designer but do it as a Hobby - by the way this is my first CAD Drawing).

Using the above formula I get the Diameter, Length of the header pipe, secondary cone etc.
When I calculate the formula I got Diameter of the Primary Pipe around 30mm.
I took 35mm as I will have bend just after the Gases Come out of the Exhaust Port. (Bend After 60mm from the Exhaust Port - Please refer Images Attached)

Figure : All Dimensions (Click the image to enlarge it )

Primary Pipe - Measurements (Please refer Images for this)
From my mock up CAD design I have taken the Main Pipe (From Exhaust Port till secondary pipe) Diameter as 35mm and length of which is around 650mm (65cms). Secondary Pipe Diameter I have taken as 45mm at the Expanded area (cone moves from 35mm diameter to 45mm diameter in about 100mm length). For the next 200-250mm I have the same Diameter of 45mm till the muffler. I have designed a slip-on muffler which gets connected to the this pipe (you can see in the CAD drawing).

Figure : Without Muffler (Click the image to enlarge it )

Figure : 3D View. (Click the image to enlarge it )

Muffler Design - Measurements ( Measurements are taken looking at the Stock Muffler on the bike - Have increased about 10% as of the stock Muffler) For the Muffler I have taken 350mm length, 100mm diameter and Exhaust output diameter without DB Killer will be 60mm (double the Exhaust Port). (ON Stock Muffler this is 20mm) With DB Killer Exhaust output diameter will be 30mm (same as Exhaust Port). (Design - UNDER PROCESS)

Exhaust pipe length and size. why we need this?.As the exhaust valve opens, a positive or pressure wave front is created which travels down the exhaust pipe at the speed of sound. As this pressure wave reaches the end of the pipe, it expands and a negative or suction pulse travels back up the pipe towards the engine.

As the negative wave front in turn reaches the cylinder, it reverses again and moves back towards the end of the pipe. This fluctuating pressure pulse effect can be used to great advantage in tuning the engine.

If the system is designed in such a way that the negative or suction pulses return to the cylinder at overlap T.D.C., then they will assist in clearing the combustion chamber of exhaust gases.In turn, this will cause a depression at the inlet valve, which will help draw in the inlet charge.

The following formula can be used to calculate the ideal length for Primary Pipe Length:LengthOfPipe = (129540 x E.T) / (R.P.M. x 6)

Where:
L = Primary pipe length in mms measured from the exhaust valve head.
E.T. = Exhaust valve duration in degrees from point of valve opening before B.D.C plus the full 180 degree stroke up to T.D.C. (Assumption*)(Reverse calculation for the stock exhaust to get this value)
R.P.M. = The estimated revs, at which max. power will be achieved minus five hundred.

Having calculated the primary pipe length, we must now calculate the diameter as follows :

Divide "L" by 10 to bring it to cms. Call this "L2". (60)
Take the cylinder capacity in ccs and double it. (Say 153 x 2 = 306)
Divide by "L2" as previously calculated. (306 / 60 = 5.1)
Divide by 3.4 (5.1 / 3.4 = 1.5)
Find the square root (√1.5 = 1.225)
Multiply by two and add 0.3 ((1.225 x 2) + 0.3 = 2.75)
Multiply by 10 to bring it back to mms. (10 x 2.75 = 28) = 26~28mms. (Diameter based on ET Values) - I have taken this as 35mm as, we don't have negative pressure from other cylinders as this is a Single Cylinder Engine.

NOTE : The Above Calculation is for Multiple Cylinder - for 4-2-1 or 4-1 Pipe configuration.
Above length is the Primary Pipe Only

*Assumption is the Mother of all f^%$-ups.

QUESTION TIME:
1. I am using the Formula LengthOfPipe = (129540 x E.T) / (R.P.M. x 6) to get the information. This formula is mainly used for Engine with more than one Cylinder. Is there a specific Formula we can use to calculate Pipe Diameter / Length for a SINGLE Cylinder Engine.
2. Also Can someone please review if my calculations are all ok.

Impressive CAD drawing for a first attempt! Helmholtz resonance tuning is what that article is all about, as far as I can tell you're on the right track here but some further reading on Helmholtz theorems certainly won't hurt. Hopefully one of the local geniuses on here will pick this up soon.

From what I understand, however, resonance tuning is not all that beneficial on 4-stroke ICE's and even less beneficial on ones that have high operational speeds (bike engines). This is due to the first and second order harmonic balances of the engine itself creating resonance frequencies that interrupt with the pulses traveling up and down the exhaust.

1. I am using the Formula LengthOfPipe = (129540 x E.T) / (R.P.M. x 6) to get the information. This formula is mainly used for Engine with more than one Cylinder. Is there a specific Formula we can use to calculate Pipe Diameter / Length for a SINGLE Cylinder Engine.

Click to expand...

This formula IS for a single cylinder engine. But first, you have to understand that there is no «magic» formula to determine exhaust length and diameter; only formulas that will give ballpark values based on experience, not scientific calculations. The approximation are usually worst for exhaust than intake tuning.

I cannot judge these equations but, as for the diameter of the exhaust pipe, you have to understand that the exhaust port diameter will be your biggest limiting dimension to determine the tuned RPM. So it is of no use to put a really large exhaust pipe if the exhaust part is small. Usually, the exhaust pipe-to-port diameter ratio is between 1.10 and 1.25.

First, your estimation for E.T. is off. This value shouldn't be below 230. Use the «Exhaust timing selection chart» on page 29-30 of the book you referred to. You most probably have a «Standard Engine» or «Stage 1 Street» engine type unless you have a racing engine.

Second, you don't need a secondary pipe. Since all numbers are approximate, let me explain to you the concepts you have to understand behind the design.

The pressure wave begins its journey at the exhaust valve. It then travels at the speed of sound throughout the pipe. The speed of sound varies with exhaust gas temperature, so the pressure wave will be slower at the end of the pipe than at the exhaust valve (It is even more complex than that, but what you have to remember is that the tuned RPM is not directly related to the pipe length; other factors are involved).

Once the pressure wave encounters an area change, it will reflect another wave back to the engine. If the area is reduced, it will reflect a pressure wave slightly smaller (if it hits a closed end, it will bounce of the end and be reflected as the full pressure wave). We don't want that.

If the pressure wave encounters a larger area, it will reflect a «suction» wave: The bigger the pressure wave and the bigger the area change, the bigger the «suction» wave. Once this «suction» wave arrives back at the engine, it will help emptying the cylinder. The largest area change possible is at the end of the pipe, where it meets the atmosphere (area is infinite at this point).

If you have a pipe going into a bigger pipe, the pressure wave will partly reflect as a «suction» wave and it will also continue its journey into the bigger pipe, slightly diminished. This slightly diminished pressure wave will also reflect another «suction» wave when it encounters another area change along the way in the bigger pipe.

Knowing all of that, here's how you have to analyze your design:

If you have an exhaust pipe of a single diameter - equal to the exhaust port diameter - and this pipe discharges directly into the atmosphere, you will have a very peaky engine, tuned for the RPM you've calculated. The drawback is that it will perform poorly at other RPM. This is how it is done for racing engine looking for maximum horsepower (like a dragster for example).

If you want a larger power band, you need to have «different» pipe lengths for the RPM range you desire. So you can increase the pipe diameter along the way. Ultimately, you can use a tapered pipe, which will reflects «suction» waves at every millimeter of your pipe. Naturally, since the area change is small at every step, the «suction» wave reflected is also small and offers less maximum power at a given RPM that a straight pipe discharging into the atmosphere.

How big of an area change do you need ? To «simulate» an atmosphere, you need a diameter change of 2,5 or bigger. So if you have a pipe of 1" in diameter discharging into a pipe of 2,5" in diameter, for the pressure wave it will feel like discharging into the atmosphere; meaning that any other area change afterward will be more or less meaningless as the pressure wave will practically completely loose its strength at this point.

Knowing all of that, you can now appreciate the flaws in your design. The change from 35 to 45 mm is not very large and it will return only a small «suction» wave. The first «true» area change the pressure wave will encounter will probably be your muffler. So your effective pipe length is more or less 1 000 mm.